Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
It is given in the question that
Ann, Chang, and Kareem sent a total of 89 text messages over their cell phones during the weekend. Ann sent 9 fewer messages than Chang. Kareem sent 3 times as many messages as Ann.
Let number of messages Chang sent be x. And Ann sent 9 fewer than Chang, so Ann sent (x-9) messages. And Kareem sent 3 times as many messages as Ann, so Kareem sent 3(x-9) messages.
And the total messages are 89. That is
Combining like terms
So Chang sent 25 messages, Ann sent
And Kareem sent
Answer:
18
Step-by-step explanation:
4 divided by 24 is 6
6x3=18
<h2><em>Find the LCD of 1/3 and 1/2.</em></h2><h2><em>The LCD is 6.</em></h2><h2><em>1/3 in 6ths is 2/6.</em></h2><h2><em>1/2 in 6ths is 3/6.</em></h2><h2><em>2/6 + 3/6 = 5/6.</em></h2><h2><em>1/3 + 1/2 = 5/6.</em></h2><h2><em>Hope this helps and have a nice day.</em></h2>
